solve for x?

Question

(sqrt3x+1) -1= x-4

Answer 1

sqrt(3x+1) -1 = x - 4
sqrt(3x + 1) = x -3
3x + 1 = (x - 3)^2 = x^2 - 6x + 9
x^2 - 9x + 8 = 0 = (x - 1) (x - 8)
x = 8 since x = 1 doesn't work unless you take the negative root.

Answer 2

if your problem actually looks like this:
sqrt(3x+1) - 1 = x-4
then this is the work:

sqrt(3x+1) = x-4+1
sqrt(3x+1) = x-3 /^2
3x+1 = (x-3)^2
3x+1 = x^2 - 2*x*3 + 3^2
3x+1 = x^2 - 6x + 9
0 = x^2 - 6x + 9 - 3x - 1 (usually we separate all the negatives on one side, and all the positives on the other, but for the convenience, we'll have them all on the same side)

0 = x^2 - 9x + 8 (now we can switch sides, because the equality works both ways)
x^2 - 9x + 8 = 0
from here, we can either use quadratic equation, or try to factor the equation, then solve for x1 and x2

let's try with factoring (more convenient - I'd like to avoid writing sqrt, etc.):
x^2 - 8x - x + 8 = 0
x(x-8) - (x-8) = 0
(x-8)(x-1)=0 (let's order them properly:)
(x-1)(x-8)=0


x-1= 0
x = 1
check:
sqrt(3x+1) - 1 = 1 - 4
sqrt (3*1 + 1) - 1 = -3
sqrt(3+1) - 1 = -3
sqrt(4) - 1 = -3 (here we'll use the fact that sqrt(4) equals both to 2 and -2)
-2 - 1 = -3
-3=-3
OK => x1 = 1

x-8 = 0
x = 8
check:
sqrt(3x+1) - 1 = x - 4
sqrt (3*8 + 1) - 1 = 8 - 4
sqrt(24+1) - 1 = 4
sqrt(25) - 1 = 4
5-1 = 4
4 = 4
OK => x2 = 8

The system works for x1 = 1, and x2 = 8
You can check with quadratic equation - you'll get the same pair of solutions, and the checking process is still the same.

Answer 3

Do you mean sqrt3x + 1 or sqrt(3x+1)?

If it is the latter then:

sqrt(3x+1)=x-3
3x+1=(x-3)^2
3x+1=x^2-6x+9
x^2-9x+8=0
(x-8)(x-1)=0
So x=8 or x=1

Answer 4

Clarify:
Is it the sqrt(3x+1) -1 = x-4 ?

If this is what you meant, move the 1 to the right side.

sqrt(3x+1) = x-3

Square both sides

3x+1 = x^2 -6x +9 (the right side is foiled when squared!)

move the 3x+1 to the right side

Solve for x.

Answer 5

All answer are incorrect or in part maximum surprising! The is a try no be counted if the equation holds. because of the fact the quotient x/x is given, the equation is defined for x=0, because of the fact the fact, that there is a real decrease for x goint to 0 of x/x: limit_x->0 x/x=a million. So do away with the quotient a minimum of for x unequal 0. The equation now is x+x²=x². This equation could be rearranged by ability of unique arithmetic operations. It provides x=0. stupid or. What does is propose? The equation does not carry for x unequal 0. this is it. it could returned be simplified a million+x=x or a million=0, this is faulty. For 0 is holds interior the stable style and interior the decrease attention: 0/0+0=a million+0 unequal 0. The equation does not be valid for any genuine numbers!

Answer 6

√(3x + 1) - 1 = x - 4

==> √(3x + 1) = x - 3
==> 3x + 1 = (x - 3)²
==> 3x + 1 = x² - 6x + 9
==> x² - 3x + 8

Ok.....you can do the rest.

:)